In a large bowl, toss together lamb, half of the oregano, 2 tablespoons lemon juice, garlic, 2 teaspoons salt and 1/2 teaspoon ground black pepper.
Heat 1 tablespoon oil in a large skillet over high heat. Add half of the lamb and cook, tossing constantly, until cooked through and liquid is absorbed, 5 to 7 minutes; transfer to a plate. Repeat process with remaining oil and lamb.
In a bowl, combine yogurt, cucumber, remaining 1 tablespoon lemon juice and salt and pepper to taste.
Arrange quinoa on a platter or individual serving plates. Spoon lamb over quinoa, top with peppers, cucumber-yogurt sauce and remaining oregano and serve.